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Abstract
We demonstrate a composite meta-surface beam former to generate reconfigurable multiple orbital angular momentum (OAM) vortex waves by integrating a polarization conversion meta-mirror with a multi-functional anisotropic meta-lens. More specifically, electromagnetic fields from the feed would be firstly reflected by the meta-mirror, and then transmit through the meta-lens to form the well converged OAM vortex waves with tailored beam numbers, radiation directions and topological charges. Especially, we show that the anisotropic characteristics of the meta-lens would create different multiple OAM vortex waves when the meta-mirror is rotated or equipped with active circuits to have different polarized illuminations on the meta-lens. Our design should pave the way for the reconfigurable design of generating multiple OAM vortex waves to further expand the communication capacity.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Orbital angular momentum (OAM) vortex waves have recently attracted enormous attentions in wireless communication for the great multiplexing capacity in increasing the spectral efficiency [1–10]. The initiation of the quest for multiple OAM vortex waves has thus emerged and should establish more advanced communication systems with expansive development foreground by combining the superiority of these two techniques.
Meta-surface has been widely applied to manipulating electromagnetic fields with tailored functionalities through a proper arrangement of subwavelength meta-atoms [11]. It can create spiral phase distributions by introducing additional component of $e^{jl\phi }$ in the synthesized vortex wave-fronts, where $l$ refers to the topological charge and $\phi$ refers to the azimuth angle [12–19]. In the meanwhile, meta-surfaces tailored with anisotropic characteristics have shown to be capable of tuning the polarization states of OAM vortex radiations by controlling reflection phases in the $x$ and $y$ polarizations directions independently [20]. Especially, the digital coding meta-surfaces with unique capability of field programming have also demonstrated perfectly synthesis of OAM vortex waves with flexibly controllable scattering properties [21–23], thus have significantly enriched the functions of meta-surfaces and the capabilities in manipulating the electromagnetic waves. Apart from that, one can further create multiple OAM vortex radiations with specific prescribed beam numbers by using the superposition of aperture fields. The meta-mirror is recommended in most scenarios as a high efficiency candidate to create multi-radiations with vortex wave-front, while the meta-lens with the same capabilities can also obtain the high-purity multiple OAM vortex waves [24–31]. In particular, the present literatures have also witnessed the implementations of multiple beams with controllable topological charges and polarization characteristics in each individual radiation [32–35]. These studies, using meta-mirrors or consulting meta-lenses, have further demonstrated the flexible regulation of electromagnetic fields for the multiple OAM vortex waves. However, all these multiple beam generations can only operate in a constant way with certain OAM vortex characteristics and the radiators at present are normally equipped with no reconfigurable designs. Clearly, if we can reformulate the multiple OAM vortex radiations on the basis of different polarizations using the same generator, it should certainly expand the channel capacity in the wireless communication to have OAM vortex waves with different polarization information coexisting over a common channel. However, it will not be easy to directly equip the single meta-lens or meta-mirror with the reconfigurable design of multiple OAM vortex waves as the meta-apertures should not only possess the adequate phase coverage for the beam forming, but also have to offer the adjustable functionalities of different polarizations. Based on these considerations, we construct a composite meta-surface beam former to generate reconfigurable multiple OAM vortex waves by combining a meta-mirror and an anisotropic meta-lens. Electromagnetic fields from the feed would be firstly reflected by the meta-mirror, and then transmitting through the meta-lens to form the well converged multiple OAM vortex waves with tailored beam numbers, radiation directions and topological charges. Different from the conventional anisotropic meta-surfaces dependent on the one layered Pancharatnam-Berry meta-units [27–32,34,35] or the resonant behaviors of gradient screw meta-atoms [36,37] that usually have spatially angular responses respecting to the $x$- and $y$-polarized electromagnetic fields from different incident angles, the meta-lens in this demonstration using multi-layered structures with non-resonant constituting elements of anisotropic rectangular patches and cross metallic stripes on the substrates can possess the merits of stable transmission properties and phase responses at certain frequency under wide-angular illuminations, while maintaining the sensitivities for different polarized electromagnetic fields. As a result, the anisotropic characteristics of the meta-lens would create different multiple OAM vortex waves when the meta-mirror is rotated or equipped with active circuits to have different polarized illuminations on the meta-lens. Our design should pave the way for devising multiple OAM vortex waves in the transmission regime and offer the proposals of generating reconfigurable multiple OAM vortex waves to further expand the communication capacity.
2. Design and numerical results
Figure 1 demonstrates the composite meta-surface beam former for generating multiple OAM vortex waves, consisting of a meta-mirror formed of rectangle ring array or PIN diode integrated butterfly array over the grounded substrate and a meta-lens composed of multi-layer meta-surfaces with anisotropic rectangular patches and cross metallic stripes on the substrates to regulate electromagnetic fields of different polarizations independently. The feed is placed at the real focal point $F_{2}$ of meta-mirror, and the virtual focal point $F_{1}$ of meta-mirror is set under the physical focal point of the meta-lens. The incidence from the feed would thus be reflected by the meta-mirror firstly, and then penetrate through the meta-lens to form the well converged OAM vortex waves with tailored beam numbers, radiation directions and topological charges. In addition, the electromagnetic waves reflected by the meta-mirror could be either $x$- or $y$-polarized, and such different polarization states can be readily obtained by rotating the meta-mirror $45^{\circ }$ along $z$-axis, or switching the active circuit of the PIN diodes, where we employ the package SMP-1320 diodes from Skyworks having the electrical performance of an 0.28 pF OFF capacitance and 0.5 $\Omega$ ON resistance. The target tri-beams in the demonstration are $\left [\begin {array}{l} \theta _{x_{i}} \\ \phi _{x_{i}} \\ l_{x_{i}} \end {array}\right ]_{i=1,2,3}=\left [\begin {array}{ccc} 30^{\circ } & 30^{\circ } & 30^{\circ } \\ 60^{\circ } & 180^{\circ } & 300^{\circ } \\ -1 & 2 & 1 \end {array}\right ]$ under the $x$-polarized incidence from the meta-mirror and $\left [\begin {array}{l} \theta _{y_{i}} \\ \phi _{y_{i}} \\ l_{y_{i}} \end {array}\right ]_{i=1,2,3}=\left [\begin {array}{ccc} -30^{\circ } & 0^{\circ } & 30^{\circ } \\ 90^{\circ } & 90^{\circ } & 90^{\circ } \\ -1 & 2 & 1 \end {array}\right ]$ for $y$-polarized incidence, where $\theta _{x_{i}}$/$\theta _{y_{i}}$, $\phi _{x_{i}}$/$\phi _{y_{i}}$ and $l_{x_{i}}$/$l_{y_{i}}$ refer to the elevation angle, azimuth angle and topological charge for the $i$th beam.
Fig. 1. Illustration of the reconfigurable multiple OAM vortex waves through the composite meta-surface beam former. (a) Configurations of the composite meta-surface beam former and ray traces, where $I_{x}$ refers to the incident $x$-polarized wave from the feed, $R_{xx}$ and $R_{yx}$ refer to the reflected $x$- and $y$-polarized wave respectively from the meta-mirror. The circular meta-mirror has the radius of 80 mm. The meta-lens has the aperture size of 480 $\times$ 480 mm$^{2}$ with the thickness of 6 mm. Unit structural information of the active meta-mirror (b), and the passive meta-mirror (c). Configuration of the multi-layered meta-lens unit (d), and its structural information (e). The physical parameters are $a=238.4$ mm, $b=170$ mm, $c=101.6$ mm, $d=0.5$ mm, $e=0.5$ mm, $f=1.1$ mm, $g=5.6$ mm, $s=2.8$ mm, $t=0.6$ mm, $u=8.45$ mm, $v=4.6$ mm, $w=0.3$ mm, $r=10$ mm, $h_{1}=3$ mm, $h_{2}=2$ mm, $h_{3}=1$ mm, $\varepsilon _{r}=4.4$.
The phase distributions of the meta-mirror $\Phi _{AM}$ and meta-lens $\Phi _{PM}$ can be calculated as
Figure 2 demonstrates the corresponding reflection and transmission of the meta-mirror and meta-lens with different structural parameters under the illuminations from different incident angles. We can observe in Fig. 2(a) the reflection amplitude $R_{xx}$ from the meta-mirror can maintain above 0.95 regardless the variations of the managing frequencies from 6 GHz to 7 GHz and incident angles from $0^{\circ }$ to $40^{\circ }$ when $\beta =0^{\circ }$, thus would generate high purity $x$-polarized reflections. At the same time, it varies with frequencies and reaches the peak at 6.8 GHz when $\beta =45^{\circ }$, and the value of reflection amplitude $R_{yx}$ can keep more than 0.9 regardless the variations of incident angles within $40^{\circ }$, indicating the perfect polarization conversion and the generation of $y$-polarized reflections from the meta-mirror. On the other hand, we can also employ the active meta-mirror to carry out the polarization conversion based on dual states of the PIN diode. As shown in Fig. 2(b), the value of reflection amplitude $R_{xx}$ at 6.8 GHz would reach the peak of 0.95 when we have the ON-state PIN diodes, and $R_{yx}$ would reach 0.9 when the PIN diodes are set to be the OFF-status. In addition, the incident angles are shown to have scarcely influence on the polarization conversion functionalities of the active meta-mirror. Figures 2(c) and 2(d) demonstrate the required transmitting phases of the meta-lens for the desired triple OAM vortex waves. The phase distribution in Fig. 2(c) superimposes the additional phases for tri-beam generation with elevation angle $\theta _{x[1,2,3]}=[30^{\circ },30^{\circ },30^{\circ }]$, azimuth angle $\phi _{x[1,2,3]}=[60^{\circ },180^{\circ },300^{\circ }]$ and topological charges $l_{x[1,2,3]}=[-1,2,1]$ when illuminated by the $x$-polarized incidence. On the other hand, the phase distribution in Fig. 2(d) possesses the information of $\theta _{y[1,2,3]}=[-30^{\circ },0^{\circ },30^{\circ }]$, $\phi _{y[1,2,3]}=[90^{\circ },90^{\circ },90^{\circ }]$ and $l_{y[1,2,3]}=[-1,2,1]$ when under the $y$-polarized incidence. Figures 2(e) and 2(f) demonstrate the phase responses and transmittance of the periodic meta-lens unit at 6.8 GHz with structural parameters $p$ and $q$ varying from 1 mm to 8.9 mm under the illuminations of $x$-polarized electromagnetic waves from different incident angles of $[0^{\circ },40^{\circ }]$, where other structural parameters of the meta-lens unit are kept constantly as in Fig. 1 during the design. We can observe that transmitting phases of the periodic meta-lens units would be capable of covering nearly $360^{\circ }$ and transmission amplitudes would keep a high level transmission, thus fulfilling the design requirements of the meta-lens implementation. Due to the symmetry of the $x$- and $y$-polarized illuminations, the phase responses and the transmittance of meta-lens under $y$-polarized illumination can readily be obtained by simply transform the coordinates.
Fig. 2. The electromagnetic responses from the meta-mirrors and the required phase distributions of the meta-lens and its synthesis. The polarization conversion performances of the passive meta-mirror (a) and active meta-mirror (b), where refer $R_{xx}$/$R_{yx}$ refer to the reflection amplitudes of the reflected $x$- or $y$-polarized electromagnetic fields from the meta-mirror under the illumination of $x$-polarized incidence. The required phase distributions of the meta-lens for the triple OAM vortex waves under the illuminations of $x$- (c) and $y$-polarized (d) incidences. The relationships between the transmitting phases (e) and amplitudes (f) between different structural parameters of the anisotropic meta-lens-unit under the illumination from $0^{\circ }\sim 40^{\circ }$.
Figure 3 continues to demonstrate the equivalent circuit model [38] of the meta-surface lens in this demonstration, where $Z_{1}=Z_{0}/\sqrt {\varepsilon _{r}}$ refers to the characteristic impedance for all the six layers, $C_{i}$ and $L_{i}$ represent the equivalent capacitors of the $i$th rectangular patch and inductors of $i$th cross patch. The parallel capacitors and inductors would thus have the following forms under the illuminations of TE/TM oblique incidence [39]
The full-wave simulations (CST Microwave Studio) are performed as shown in Fig. 4 to verify the composite meta-surface beam former integrated with the passive meta-mirror. We can observe that the composite meta-surface beam former achieves $x$-polarized vortex waves in the directions of $\left [\begin {array}{lll} \theta _{x1} & \theta _{x2} & \theta _{x3} \\ \phi _{x1} & \phi _{x2} & \phi _{x3} \\ l_{x1} & l_{x2} & l_{x3} \end {array}\right ]=\left [\begin {array}{ccc} 30^{\circ } & 30^{\circ } & 30^{\circ } \\ 60^{\circ } & 180^{\circ } & 300^{\circ } \\ -1 & 2 & 1 \end {array}\right ]$ and $y$-polarized vortex waves in $\left [\begin {array}{lll} \theta _{y1} & \theta _{y2} & \theta _{y3} \\ \phi _{y1} & \phi _{y2} & \phi _{y3} \\ l_{y1} & l_{y2} & l_{y3} \end {array}\right ]=\left [\begin {array}{ccc} -30^{\circ } & 0^{\circ } & 30^{\circ } \\ 90^{\circ } & 90^{\circ } & 90^{\circ } \\ -1 & 2 & 1 \end {array}\right ]$. For the $x$-polarized vortex waves, the maximum gains are 11.49 dBi at $\phi =60^{\circ }$, $\theta =25^{\circ }$, 10.83 dBi at $\phi =180^{\circ }$, $\theta =39^{\circ }$, 12.76 dBi at $\phi =300^{\circ }$, $\theta =35^{\circ }$ and the corresponding $y$-polarized vortex waves in $\phi =90^{\circ }$ are 12.24 dBi at $\theta =-26^{\circ }$, 9.38 dBi at $\theta =-6^{\circ }$, 11.95 dBi at $\theta =25^{\circ }$. The amplitude patterns and phase patterns of the $x$- and $y$-polarized vortex waves are demonstrated at 2750 mm away from the meta-lenses with a scanning range of 1400 $\times$ 1400 mm$^{2}$. The amplitude distributions show a circular distribution with a central defect singularity, while the phase patterns show a $360^{\circ }$ phase change around center of the radiation aperture as we expected. Clearly, these results show that the proposed composite meta-surface beam former radiate tri-beams with mode number of $l = -1, 2, 1$.
Fig. 4. Triple beams from the composite meta-surface beam former with the passive meta-mirror at 6.8 GHz. The radiation patterns of the vortex waves with $x$- (a) and $y$-polarized (b) illuminations from the passive meta-mirror. The amplitude patterns and phase patterns of vortex waves at 2750 mm away from the meta-lenses with a scanning range of 1400 $\times$ 1400 mm$^{2}$ with $x$- (c) and $y$-polarized (d) illuminations from the passive meta-mirror. The mode purity of the vortex waves with $x$- (e) and $y$-polarized (f) illuminations from the passive meta-mirror.
We continue to investigate the mode purity of the OAM waves with the Fourier relationship between the OAM spectrum $P$ and the phase distribution of electric fields $\Psi$ having the form of
where $P$ and $\Psi$ refer to the OAM spectrum and phase value of electric fields, $\phi$ and $l$ stand for the azimuth angle and topological charges. We can observe that the generated $x$-polarized vortex waves with $l = -1, 2, 1$ having the mode purities of $82\%$, $74\%$, $83\%$ and the corresponding $y$-polarized vortex waves with $l = -1, 2, 1$ possessing the mode purities of $89\%$, $63\%$, $89\%$ respectively.Figure 5 demonstrates the composite meta-surface beam former integrated with the active meta-mirror, where the synthesized $x$-polarized and $y$-polarized vortex waves should be in the same directions as the one with the passive meta-mirror since the meta-lens remains unchanged in both systems. For the $x$-polarized vortex waves radiation, the maximum gains are shown to be 11.46 dBi at $\phi =60^{\circ }$, $\theta =25^{\circ }$, 10.46 dBi at $\phi =180^{\circ }$, $\theta =39^{\circ }$, 12.49 dBi at $\phi =300^{\circ }$, $\theta =35^{\circ }$ and the corresponding $y$-polarized vortex waves in $\phi =90^{\circ }$ turn out to be 11.94 dBi at $\theta =-26^{\circ }$, 8.8 dBi at $\theta =-8^{\circ }$, 11.79 dBi at $\theta =25^{\circ }$. The amplitude patterns and phase patterns of the $x$- and $y$-polarized vortex waves are presented in a similar way as the one with the passive meta-mirror. We can also observe that the generated $x$-polarized vortex waves with $l = -1, 2, 1$ have the mode purities of $77\%$, $75\%$, $79\%$ and the corresponding $y$-polarized vortex waves with $l = -1, 2, 1$ possess the mode purities of $85\%$, $66\%$, $78\%$ respectively, which are a little bit lower than those with the passive meta-mirror due to non-perfect responses from the active meta-mirror. However, the overall radiation performances of both the composite meta-surface beam formers have all achieve the reconfigurable designs of the multiple OAM vortex wave generations with different topological charges and radiation directions.
Fig. 5. Triple beams from the composite meta-surface beam former with the active meta-mirror at 6.8 GHz. The radiation patterns of the vortex waves with $x$- (a) and $y$-polarized (b) illuminations from the active meta-mirror. The amplitude patterns and phase patterns of vortex waves at 2750 mm away from the meta-lenses with a scanning range of 1400 $\times$ 1400 mm$^{2}$ with $x$- (c) and $y$-polarized (d) illuminations from the active meta-mirror. The mode purity of the vortex waves with $x$- (e) and $y$-polarized (f) illuminations from the active meta-mirror.
Figure 6 continues to demonstrates the split dual OAM vortex waves from the composite meta-surface beam former. The split beams in the demonstration are $\left [\begin {array}{l} \theta _{x_{i}} \\ \phi _{x_{i}} \\ l_{x_{i}} \end {array}\right ]_{i=1,2}=\left [\begin {array}{cc} 30^{\circ } & 30^{\circ } \\ 45^{\circ } & -45^{\circ } \\ -1 & 1 \end {array}\right ]$ under the $x$-polarized incidence from the meta-mirror and $\left [\begin {array}{l} \theta _{y_{i}} \\ \phi _{y_{i}} \\ l_{y_{i}} \end {array}\right ]_{i=1,2}=\left [\begin {array}{cc} 30^{\circ } & 30^{\circ } \\ 135^{\circ } & -135^{\circ } \\ -1 & 1 \end {array}\right ]$ for $y$-polarized incidence. Figures 6(a) and 6(b) demonstrate the required transmitting phases of the meta-lens for the desired split dual OAM vortex waves. For the composite meta-surface beam former with passive meta-mirror, the maximum gains are 12.40 dBi at $\phi =45^{\circ }$, $\theta =26^{\circ }$, 13.75 dBi at $\phi =-45^{\circ }$, $\theta =37^{\circ }$ for the $x$-polarized vortex waves. Meanwhile, the maximum gains are 13.56 dBi at $\phi =135^{\circ }$, $\theta =24^{\circ }$, 13.86 dBi at $\phi =-135^{\circ }$, $\theta =26^{\circ }$ for the corresponding $y$-polarized vortex beams. On the other hand, for the composite meta-surface beam former with active meta-mirror, the maximum gains are 12.83 dBi at $\phi =45^{\circ }$, $\theta =26^{\circ }$, 13.44 dBi at $\phi =-45^{\circ }$, $\theta =37^{\circ }$ for the $x$-polarized vortex waves. Meanwhile, the maximum gains are 14.68 dBi at $\phi =135^{\circ }$, $\theta =25^{\circ }$, 13.96 dBi at $\phi =-135^{\circ }$, $\theta =26^{\circ }$ for the corresponding $y$-polarized vortex beams. We can also observe that the $x$-polarized vortex waves from the composite meta-surface beam former with passive meta-mirror have the mode purities of 86% and 87% for $l=-1$ and 1 respectively. The corresponding $y$-polarized vortex waves with $l=-1$ and 1 are possessing the mode purities of 81% and 83%. On the other hand, the composite meta-surface beam former with the active meta-mirror would generate $x$-polarized split vortex waves with the mode purities of 84% and 79% for $l = -1$ and 1. In the meanwhile, the corresponding $y$-polarized vortex waves with $l = -1$ and 1 would possess the mode purities of 82% and 79% respectively.
Fig. 6. Polarization induced reconfigurable split dual beams from the composite meta-surface beam former with the passive and active meta-mirror at 6.8 GHz. The required phase distributions of the meta-lens for split dual OAM vortex waves under the illuminations of $x$- (a) and $y$-polarized (b) incidences. The radiation patterns of the vortex waves with the passive (c) and active (d) meta-mirror. The amplitude patterns and phase patterns of vortex waves at 2750 mm away from the meta-lenses with a scanning range of 1400 $\times$ 1400 mm$^{2}$ with the passive (e) and active (f) meta-mirror. The mode purity of the vortex waves with passive (g) and (g) active meta-mirror.
3. Fabrication and experimental results
Finally, we fabricate the proposed composite meta-surface beam former and experientially test the radiation performances as demonstrated in Fig. 7. In the experiment, the F4B circuit board ($\varepsilon _{r}=4.4$, $tan\delta =0.0033$) is chosen as the dielectric substrate. The composite meta-surface beam former is tested at 2750 mm away from the probe with a scanning range of 800 $\times$ 800 mm$^{2}$. The phase distributions show spiral distribution around the center are all agree with our devised OAM waves having mode numbers of $l = -1, 2, 1$. Table 1 demonstrates mode purity comparisons between the vortex waves from the measurements and simulations. The vortex waves from the measurement with $l = -1, 2, 1$ are having the mode purities of $72\%$, $65\%$, $78\%$ for the $x$-polarized radiations, and possessing the mode purities of $81\%$, $55\%$, $73\%$ for the $y$-polarized emissions when the meta-lens is integrated with the passive meta-mirror. On the other hand, the vortex waves from the measurement with $l = -1, 2, 1$ would have the mode purities of $70\%$, $64\%$, $72\%$ for the $x$-polarized radiations, and possessing the mode purities of $82\%$, $55\%$, $67\%$ for the $y$-polarized emissions when the meta-lens cooperates with active meta-mirror.
Fig. 7. The manufactured photos and the measurement results. (a) The experimental setup of the composite meta-surface beam former with the passive (a) and active (b) meta-mirror. Magnified pictures of the meta-lens (c), passive meta-mirror (d) and active meta-mirror (e). The phase distribution of the vortex radiations at 2750 mm from the composite meta-surface beam former with the passive (f) and active (g) meta-mirrors.
Table 1. Mode purity comparisons between vortex waves from measurements and simulations
The radiation patterns of the proposed composite meta-surface beam former with passive and active meta-mirror are also tested as demonstrated in Fig. 8 and Table 2. In the experiments, we rotate the composite meta-surface beam former to calibrate the released vortex waves to the probe and test the radiation patterns. The $x$-polarized radiations from the composite meta-surface beam former are 10.12 dBi of $l = -1$ at $\phi =60^{\circ }$, $\theta =28^{\circ }$, 10.05 dBi of $l = 2$ at $\phi =180^{\circ }$, $\theta =42^{\circ }$, 11.36 dBi of $l = 1$ at $\phi =300^{\circ }$, $\theta =35^{\circ }$ with the passive meta-mirror and 10.02 dBi of $l = -1$ at $\phi =60^{\circ }$, $\theta =15^{\circ }$, 9.87 dBi of $l = 2$ at $\phi =180^{\circ }$, $\theta =41^{\circ }$, 10.95 dBi of $l = 1$ at $\phi =300^{\circ }$, $\theta =38^{\circ }$ when integrated with the active meta-mirror. On the other hand, the corresponding $y$-polarized radiating vortex waves from the composite meta-surface beam former are 11.78 dBi of $l = -1$ at $\theta =-27^{\circ }$, 8.81 dBi of $l = 2$ at $\theta =-5^{\circ }$, 11.12 dBi of $l = 1$ at $\theta =26^{\circ }$ with the passive meta-mirror and 10.89 dBi of $l = -1$ at $\theta =-28^{\circ }$, 7.97 dBi of $l = 2$ at $\theta =-7^{\circ }$, 10.98 dBi of $l = 1$ at $\theta =28^{\circ }$ when cooperating with the active meta-mirror. The measurement results experience slight gain degradations compared to the simulations, and these are mainly attributing to the fabrication tolerance of the meta-surfaces, also the calibrations for the multiple vortex waves measurement in the experiments. However, the overall radiation performances are still satisfactory with different multiple OAM vortex waves as we devised.
Fig. 8. The comparisons between the measurement results and the simulation results of the composite meta-surface beam former. The x-polarized radiating patterns in (a), (b) $\phi =60^{\circ }$, (c), (d) $\phi =180^{\circ }$ and (e), (f) $\phi =300^{\circ }$ planes when integrated with passive and active meta-mirror. The $y$-polarized radiating patterns in $\phi =90^{\circ }$ plane when integrated with passive (g) and active (h) meta-mirror.
Table 2. Peak gain comparisons between vortex waves from measurements and simulations
4. Conclusions
In conclusion, we have proposed the composite meta-surface beam former for the reconfigurable multiple OAM vortex waves with different polarization states, topological charges and radiation directions. By integrating the polarization conversion meta-mirror with multi-functional anisotropic meta-lens, we have demonstrated the meta-lens can create different multiple OAM vortex waves when the meta-mirror is rotated or equipped with active circuits to have different polarized illuminations on the meta-lens. We expect the present design would pave the way for the reconfigurable design of multiple OAM vortex waves and further expand the communication capacity.
Funding
National Natural Science Foundation of China (61301072, 61671344).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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